1. **State the problem:** We need to compare two sets of data representing the circumference of balloons from two biomass mixtures: pure cow manure and cow manure with mashed bananas. We want to determine which description best summarizes the sample results based on measures of center and variability. 2. **Data given:** - Pure Cow Manure Biomass: 10, 11, 13, 13, 14, 15, 15, 15, 18, 18, 19, 20, 22, 25, 26 - Cow Manure + Mashed Bananas Biomass: 22, 22, 26, 29, 30, 31, 36, 36, 38, 39, 43, 46, 46, 49, 50 3. **Calculate the range for each data set:** - Range formula: $$\text{Range} = \text{Maximum} - \text{Minimum}$$ - Pure Cow Manure range: $$26 - 10 = 16$$ - Cow Manure + Bananas range: $$50 - 22 = 28$$ 4. **Calculate the median (measure of center) for each data set:** - Since there are 15 data points, median is the 8th value when data is ordered. - Pure Cow Manure median: 15 (8th value) - Cow Manure + Bananas median: 36 (8th value) 5. **Interpretation:** - The range for cow manure + bananas (28) is larger than for pure cow manure (16), so variability is greater in the mixture. - The median circumference is higher for the mixture (36 cm) than for pure manure (15 cm), indicating more biogas produced on average. 6. **Conclusion:** - The range is NOT about the same; it is larger for the mixture. - The mixture produces MORE biogas overall. Therefore, the best description is: **"The range is MORE CONSISTENT with pure cow manure, but the mixture of cow manure and mashed bananas creates MORE biogas overall."**